1. Motion Segmentation CAGD&CG Seminar Wanqiang Shen 2008-04-09

2. Application

3. Motion analysis Initialization Motion detection Motion tracingPose estimationRecognition Motion segmentation

4. Problem Motion segmentation projections clusters How much What How Accurate Robust Fast

5. Traditional model A rigid-body motion Multiple rigid-body motions

6. Paper [1] R. Vidal, Y. Ma, and S. Sastry. Generalized Principal Component Analysis (GPCA). IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(12):1–15, 2005. [2] J. Yan and M. Pollefeys. A general framework for motion segmentation: Independent, articulated, rigid, non-rigid, degenerate and non-degenerate. In European Conference on Computer Vision, pages 94–106, 2006. [3] R. Tron and R. Vidal: A Benchmark for the Comparison of 3-D Motion Segmentation Algorithms. IEEE International Conference on Computer Vision and Pattern Recognition, 2007.

7. [1] GPCA Model Estimating n Estimating subspacesOptimizing & clustering

8. [1] Model

9. [1] Estimating n

10. [1] Estimating subspaces calculating normalized C Factorization  Solving for the last 2 entries of each b i  Solving for the first K-2 entries of each b i

11. [1] Optimizing & clustering

12. [1] example

13. [1] Remarks Advantages  Algebraic algorithm  Dealing with both independent and dependent motions disadvantages  Deteriorating as n increases  C is sensitive to outliers

14. [2] LSA clustering projection local subspace estimation SVD

15. [2] Projection

16. [2] Local subspace estimation Affinity matrix

17. [2] Clustering Estimation N While Numofclusters< N  Compute affinity matrix for each clusters  Divide each cluster into two clusters  Evaluate the best subdivision

18. [2] examples

19. [2] Remarks Advantages  Outliers are likely to be “ rejected ”  Need less point trajectories disadvantages  Neighbors of a point belong to different subspace  The select neighbors may not span the underlying subspace

20. [3] test samples checkerboardtrafficarticulated

21. [3] Benchmark

22. [3] comparing data accuracyGPCALSA Check.6.09%5.71% Traffic1. 41%3.75% Articul.2.88%4.38% All4.59%5.09% timeGPCALSA Check.353ms7.762s Traffic288ms6.787s Articul.224ms4.002s All324ms7.165s Two groups Three groups accuracyGPCALSA Check.31.95%18.09% Traffic19.83%26.05% Articul.16.85%15.18% All28.66%19.51% timeGPCALSA Check.842ms17.314s Traffic529ms12.746s Articul.125ms1.288s All738ms15.485s

23. Thank you!